The following is the response of the maraji’ to this question:
If one’s child is poor and currently cannot earn his sustenance through a means befitting his status and state, his father is responsible for his (the son) and his (the son’s) children’s sustenance, given that he (the father) is financially established himself, while sustaining his (the son’s) wife is not his obligation. But the son must not be careless in earning a living, if he is, there is no obligation on the father.
Nafaqah, 6895 (site: 6981).
The obligation of the father’s sustenance on his son, 9970 (site: 9937).
 An istifta’ from the offices of Grand Ayatullahs: Khamenei, Sistani, Makarem Shirazi, Saafi Golpaygani (may Allah prolong all their lives), via the IslamQuest website.